In this work, we make the following contributions:
(1)
We investigate the largely ignored efficiency limitation with existing SGMs.
To that end, we provide an orthogonal invariance analysis to prove that previous SGMs are insensitive to the order of coordinates.
Further, we identify increasing the similarity between the target data distribution and these diffusion related distributions serves as an underlying contributor for convergence
(Theorem REF ).
(2)

Under this finding, we propose a Target Distribution Aware Sampling (TDAS) approach to improving the convergence efficiency of existing SGMs.

(3)

We further instantiate a specific diffusion process with
the proposed TDAS for image generation by exploiting the structural distributional priors in both frequency and space domains.
(4)

Extensive experiments demonstrate the advantages of TDAS for (NCSN [1]} and NCSN++ [2]}) in generating quality images at a variety of (\(32\times 32\)  to \(1024 \times 1024\) ) resolutions.
Critically, for more challenging high resolution image generation tasks, TDAS can reduce up to \(20\times \)  sampling iterations and accelerate the running speed by up to \(18.4\times \)  whilst largely maintaining the generation quality.
Particularly, TDAS can generate much better images in smaller sampling number cases (Fig. REF ).
